In categorical syllogisms, the quality of the conclusion follows the quality of the premises. When both premises are affirmative, the conclusion must also be affirmative. This is seen in the standard Barbara form: All S are M and All M are P, therefore All S are P. The chain of inclusions from subject through the middle term to the predicate preserves affirmation, so the conclusion remains affirmative. This rule is about the propagation of affirmation through a syllogism. The other statements describe different, separate constraints: two negative premises lead to no valid conclusion in standard syllogistic, the middle term must be distributed at least once is a structural requirement, and if a premise is negative, the conclusion must be negative. These are distinct rules and do not address the scenario described.

In traditional syllogistic, the Fourth Law of Opposition governs how a universal proposition and its corresponding particular relate in truth-value. It shows that the universal and the particular can align in different ways, but with clear conditions. If the particular statement is false, the universal must be false. That is, saying “Some S are P” is false rules out the claim “All S are P.” So a false particular forces the corresponding universal to be false. If the universal is true, the particular must be true. If “All S are P” holds, then certainly “Some S are P” holds as well, so the universal’s truth guarantees the particular’s truth. They may both be true (when the universal is true, the particular is true as well) or both be false (in some cases where neither statement can be established, especially under the traditional logic’s existential import). When neither of the above conditions applies, their statuses are indeterminate. This combination—the entailments in the second and third points plus the SAMPLEpossibility of both true or both false and the potential indeterminacy—is captured by the statement describing the Fourth Law.

In categorical syllogisms, the major term is the one that appears as the predicate in the conclusion. Here, the conclusion is “All S are P.” What’s being asserted about every S is that they are P, so the term being predicated of S is P. That makes P the major term. The subject term is S, and the middle term (the term that links the premises) would be the remaining term involved in the full syllogism. So the major term is P.

In a standard syllogism, the minor term is the subject of the conclusion. The usual labeling designates S as the subject term, P as the predicate term of the conclusion, and M as the middle term that appears in both premises but not in the conclusion. Since the conclusion makes a claim about the subject term, that subject is the minor term, so S is the minor term. The major term is the predicate of the conclusion (P), and the middle term is M, which connects the premises but doesn’t appear in the conclusion. The symbol Q isn’t used as a term in a standard syllogism.